A note on the stability of iteration procedures for strong pseudocontractions and strongly accretive type equations (Q1589729)

In Indian J. Pure Appl. Math. 28, No. 8, 1017-1029 (1997; Zbl 0898.47047) the author proved that certain Mann and Ishikawa iteration procedures are stable with respect to Lipschitz strong pseudocontractions in real Banach spaces. In J. Math. Anal. Appl. 230, 1-10 (1999; Zbl 0921.47053), \textit{H. Y. Zhou} studied, in real uniformly smooth Banach spaces, iteration methods stable with respect to strong pseudocontractions. The author proves by means of a simple example that the main result of Zhou is false without Lipschitz assumptions.